1. Field of the Invention
The invention relates generally to the field of measurements of Earth's gravity.
More particularly, the invention relates to gravity survey and interpretation techniques used to generate a three-dimensional image of gravitational acceleration and density.
2. Background Art
Certain types of geophysical measurements are used to identify the boundaries of a subsurface volume having a property of interest whose value is different from its surroundings. Such subsurface volumes may be associated with the presence of economically useful materials such as hydrocarbons. Reflection seismic surveying has been widely used for such purposes, but as requirements for resolution of spatial distribution of the selected property and depth in the subsurface of such volumes have increased, and the range of subsurface conditions has expanded to include formations such as salt and basalt, voids, fluid movement and other factors that affect the seismic response, it has become important to augment reflection seismic data with other geophysical data such as gravity.
One technique used for interpretation of geophysical data is known as inversion. In the most general sense, inversion includes generating a “model” or an initial estimate of spatial distribution of one or more properties of interest in a subsurface volume of interest. An expected response of a geophysical measuring system, such as a seismic survey system, is generated from the model. Such estimation may be referred to as forward modeling. The forward modeled system response is compared to measurements. Parameters of the initial model may be adjusted, the forward model generation may be repeated, and comparison of the repeated forward model to the measurements may be repeated until differences between the forward model and the measurements fall below a selected threshold or reach a minimum.
In the interpretation of multiple forms of geophysical measurement data, it would be advantageous to have inversion procedures that have similar formulations of the inverse problem regardless of the type of geophysical data to be inverted. This allows models to be coupled, as long as the data have comparable spatial support. One of the simplest methods uses the geophysical data sequentially during the inversion process, that is, one type of geophysical data is inverted first, followed sequentially by a similar or the same inversion procedure applied to one or more different types of geophysical survey data. The foregoing approach treats the sets of geophysical data separately. For instance, for inversion of the seismic and the gravity data, the cooperative (or sequential) algorithm uses the seismic model computed by the previous iteration to constrain the gravity model at the current iteration. This process will be repeated until convergence of the inversion procedures takes place and the final models are consistent with each other.
Another method is based on the simultaneous minimization of a misfit, error or “objective” function that includes the data of each geophysical data type. The principle feature of such technique consists in introducing an equation connecting various physical parameters of the petrophysical media, such as density, seismic velocity and resistivity. The foregoing method has received considerable attention among geophysical data users. Multiple geophysical data that are sensitive to different physical quantities may be simultaneously inverted by minimizing an objective function that includes the data misfit of different data types where the solution is constrained around a petrophysical relationship. However, petrophysical links between geophysical properties, at a specific site, are in many cases unknown as they are affected by a multitude of rock properties so determination of this relationship represents the most difficult task for this method. Other types of relationships have been introduced to avoid the parameterization of the petrophysical relationships.
While gravity brings independent information to the geophysical inversion problem, gravity data are typically sparse. Further, because gravity measurements are the measurement of a potential field, inversion of gravity data frequently results in non-unique solutions. There exists a need for an inversion technique for three-dimensional gravity survey data that makes optimum use of combinations of gravity and seismic data, and surface and borehole gravity data, in order to overcome the sparseness of data and non-uniqueness of inversion solutions.